Linear and Nonlinear Control Approaches for the Cart Inverted Pendulum Problem

This paper presents a complete review of the cart inverted pendulum (CIP) problem. The design, modeling, and control of such system as well as the implementation of a mechatronic prototype are herein presented. Several linear and nonlinear approaches such as PD, PID, and adaptive control are proposed to stabilize the system. Both theoretical and experimental performances are compared to evaluate the precision of the mathematical formulations. The aim of this study is to serve as a tutorial or supporting material for understanding the dynamics governing this system together with the potential control strategies.